Advertisements
Advertisements
Question
Rewrite the following statement without using the connective ‘If ... then’.
If it rains then the principal declares a holiday.
Advertisements
Solution
Let p : It rains.
q : The principal declares a holiday.
The given statement is p → q.
But p → q ≡ ~p ∨ q.
∴ The given statement can be written as ‘It does not rain or the principal declares a holiday’.
APPEARS IN
RELATED QUESTIONS
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Construct the truth table of the following statement pattern.
p → [∼ (q ∧ r)]
Construct the truth table of the following:
p → (q → p)
Construct the truth table of the following:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Express the following statement in symbolic form.
I like playing but not singing.
Write the negation of the following statement.
2 + 3 ≠ 5
Write the following statement in symbolic form.
If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [(~ p ∨ s) ∧ (~ q ∧ r)]
If p and q are true and r and s are false, find the truth value of the following compound statement.
[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]
State whether the following statement is True or False:
The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Mona likes Mathematics and Physics.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The necessary condition for existence of a tangent to the curve of the function is continuity.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that intelligent persons are neither polite nor helpful.
Rewrite the following statement without using the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
Write the negation of the following statement.
7 is prime number and Tajmahal is in Agra.
Negation of p → (p ˅ ∼ q) is ______
A biconditional statement is the conjunction of two ______ statements.
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
